Biggest Slice

You are sharing a large, circular pizza with $n-1$ of your friends. Your technique
for slicing the pizza is shown in Figure 1; you rotate the
pizza clockwise about its center by angle $\theta $, and then you make a slice
from the center of the pizza straight to the right. You repeat
this process, rotating by the same angle $\theta $ and slicing to the right
until you have done it a total of $n$ times.

Figure 1: Rotate-and-slice pizza division technique.

Of course, this isn’t really a good way to divide a pizza
(unless $\theta $ is
well-chosen). Some of the resulting slices may be larger than
others, and you may not even end up with $n$ different slices. You don’t care
so much about fairness. You just want to know how big the
largest slice will be, so you can take it for yourself.

Input

Input begins with an integer $1 \leq m \leq 200$ indicating the
number of test cases that follow. The following $m$ lines each contain one test case.
Each test case gives the pizza radius in centimeters,
$r$, followed by the
number of people sharing the pizza, $n$, followed by the rotation angle,
$\theta $. The quantities
$r$, $n$ and $\theta $ are all positive. The value
$r$ is an integer no
greater than 100, and $n$
is an integer no greater than $10^8$. The angle $\theta $ is given as an integer
number of degrees, followed by an integer number of minutes and
an integer number of seconds. Degrees are between 0 and 359
(inclusive), while minutes and seconds are between 0 and 59
(inclusive).

Output

For each test case, print the area in square centimeters of
the largest resulting slice of pizza. You do not need to worry
about the precise formatting of the answer (e.g. number of
places past the decimal), but the absolute error of your output
must be smaller than $10^{-4}$.